A mixture of acetone and methanol can be separated by

Fractional distillation

The correct answer is option 3. Fractional distillation.

To understand why fractional distillation is the appropriate method for separating a mixture of acetone and methanol, let's delve into the principles and applications of the distillation techniques mentioned:

Properties of Acetone and Methanol:

Acetone:

Boiling point: ≈56°C

Chemical formula: \(CH_3COCH_3\)

Methanol:

Boiling point: ≈65°C

Chemical formula: \(CH_3OH\)

The boiling points of these two substances are relatively close but distinct enough to allow separation by distillation.

Distillation Techniques:

1. Vacuum Distillation:

Lowers the boiling points of components by reducing the pressure, making it suitable for separating substances with very high boiling points or thermally sensitive compounds. Not necessary for acetone and methanol because their boiling points are not excessively high and they are not thermally sensitive under normal distillation conditions.

2. Steam Distillation:

Uses steam to distill compounds that are immiscible with water and have high boiling points. It is often used for essential oils and other compounds that might decompose at their boiling points. Acetone and methanol are miscible with each other and do not require the use of steam to lower the boiling point. This method is inappropriate for separating these two liquids.

3. Fractional Distillation:

Separates components of a mixture based on differences in their boiling points. A fractionating column is used to provide multiple condensation and vaporization steps, enhancing the separation of components with closer boiling points. The boiling points of acetone (56°C) and methanol (65°C) are sufficiently close that simple distillation would not efficiently separate them. The fractionating column in fractional distillation allows for repeated cycles of condensation and vaporization, effectively separating the two substances based on their boiling points.

Process of Fractional Distillation:

Heating the Mixture: The mixture of acetone and methanol is heated in a distillation flask.

Vaporization: As the mixture heats up, acetone, having the lower boiling point, vaporizes first.

Fractionating Column: The vapor enters the fractionating column, which contains packing material that provides a large surface area for multiple condensation and vaporization cycles.

Separation: As the vapor ascends the column, it becomes progressively richer in the lower boiling component (acetone). Methanol, with its higher boiling point, condenses and falls back into the flask, while acetone continues to rise.

Collection: The acetone vapor eventually reaches the top of the column and passes into the condenser, where it is cooled and collected as a liquid in a separate container. Methanol can then be collected after acetone is completely distilled.

Conclusion:

Given the close but distinct boiling points of acetone and methanol, fractional distillation is the most suitable method for their separation. It efficiently separates components with closer boiling points through the use of a fractionating column, ensuring a higher degree of separation and purity of the individual components.

Thus, the correct answer is: (3) Fractional distillation